The government is aiming to reverse the growing culture of unpaid internships, which favour the wealthy and well-connected, as part of a social mobility strategy to be launched by Nick Clegg.

The national internship scheme will ask firms to pay young people doing work experience and warn they could otherwise risk a legal challenge under the national minimum wage legislation. The deputy prime minister will say that the aim is to make career progression less dependent on "who your father's friends are".

The Conservative party chair, Lady Warsi, will announce on Tuesday that the civil service will end informal internships before 2012. They will all then be advertised on the government's website.

As one part of a many-pronged effort to narrow differences in achievement between social groups, a number of firms have been enlisted to give people without family connections experience in competitive fields of work. The government will encourage firms to use name-blank and school-blank applications.

The government will signal that legislation on the payment of the national minimum wage should be taken more seriously. People will be encouraged to blow the whistle on unpaid internships.

In advance of the strategy's launch, Clegg and Iain Duncan Smith, the work and pensions secretary, say in a joint article in today's Telegraph that many families are seeing their aspirations for their children dashed because private education is out of their reach and they lack the right connections.

Along with pledging to improve social mobility among those from poorer backgrounds, they say that millions of middle-income parents are also not rich enough to insulate their children against life's misfortunes.

"We want a society in which success is based on what you know, not who you know or which family you are born into," they write. "So our social mobility drive is aimed at helping the majority of people to move up the rungs of the ladder of opportunity."

Denying suggestions that the strategy will involve "social engineering", they cast their drive to open up internships as a way of preventing "the lucky few grabbing all the best chances".

"This is mobility for the middle, not just the bottom," they add.

Research shows that in Britain the influence of parental income on earnings is among the strongest in the OECD. Parental income has more than one and a half times the impact on male earnings in Britain than in Canada, Germany or Sweden.

The strategy is expected to include seven annual indicators to help the government monitor social mobility.

Clegg will say: "For too long, internships have been the almost exclusive preserve of the sharp-elbowed and the well-connected. Unfair, informal internships can rig the market in favour of those who already have opportunities.

"We want a fair job market based on merit not networks. It should be about what you know, not who you know."

Lawyers Allen & Overy; management consultants PWC and KPMG; media groups Channel 4 and the Guardian; and the Royal Institute of British Architects have agreed to offer placements and pay the national minimum wage or "reasonable out-of-pocket expenses" for any work done in their offices.

As part of a "business compact on social mobility" companies will be required to work with local schools, giving staff time off to mentor children. As a result, 100,000 adults established in their careers should go into schools at least once a year to talk about their work. Firms must also advertise work experience in schools.